If you have a car and you like Japanese food, check out Little Osaka (Sawtelle Blvd. between Santa Monica Blvd. and Olympic Blvd., roughly). My favorite places there are Tsujita/Tsujita ANNEX for tsukemen and ramen and Kiriko for Sushi. Here's a thread: http://chowhound.chow.com/topics/871694

Speaking of sushi, my favorite sushi restaurant in town, Shunji Japanese Cuisine, is on the border of Santa Monica and West Los Angeles. Too many threads to post, just do a search for Shunji.

Maybe Koreatown for Korean fare or the San Gabriel Valley for Chinese fare. Again, multitudes of threads.

For a local place for breakfast, brunch or lunch, try Weho Bistro on La Cienega @ Holloway. Very French in concept, definitely very good and reasonably priced food for regular meals, not that special occasion.

Since you are going to be right in the neighborhood, and seeing as how L.A. is the home of "bigger than life BIG SCREEN dreams where nothing succeeds like excess" you really ought to eat one breakfast at The Griddle Cafe http://www.thegriddlecafe.com/ on Sunset Blvd. (their street location is so very apropos).